If you DIY your own speakers and sell them occasionally, can you put your own brand name on them if you use well known drivers or do you have to make your own drivers to put your own brand name on your speaker?

Many (most) manufacturers use parts made by other manufacturers. As long as your brand name is not already in use by someone else it is OK. You may even find the same finished product(essentially) rebadged for different manufacturers, although they often try to ensure that theirs is unique in some way

Usually name-brand speakers are used with your own brand on them.
Where one gets in trouble is using the speaker brandname without permission.
Such as Peerless speaker system by Mybrand.
Use Mybrand model x instead.

Just a further thought: if these are DIY speakers, there's no problem with giving it a model (not brand) name and naming the drivers. It's done all the time.

If you are contemplating a commercial venture... I don't like the idea of "name-dropping". To me it seems amateurish. Personal opinion. I doubt, though, that there would be a problem in saying that this Brand X speaker is a development/fruition of your old Model Y that used Brand Z drivers(?). But I don't know for sure...